Adults, Mathematics and Work

From Research into Practice

Adults use mathematics extensively in work even though they may deny it or dismiss their numerate behaviour as common sense. Their capacity for mathematics is invisible to them and confirms their ‘non-maths person’ self-perception, which has negative consequences for their life choices. In Adults, Mathematics and Work, the authors tackle and explain a number of paradoxes related to the curious relationship between adults and mathematics. It operationalises the benefits of workplace doctoral research by providing a set of the tools to review this mistaken self-perception in order to make workers’ abilities available for development. It also provides a systematic way of uncovering and recognising informal and non-formal learning to support employability and re-employability in an increasingly fluid work-landscape.

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Biographical Note

John J. Keogh, PhD (2013), after a 30 year career in Shipping, now lectures in Mathematics and Statistics. His research interest is mathematics in work and he published Work Based Learning in the Further Education & Training Sector (Keogh, 2016).

Theresa Maguire, PhD (2003), University of Limerick, has a lifelong passion for adult mathematics education. She has worked with the National Awards Council and at the academic/employer interface. She is currently Director of the National Forum for the Enhancement of Teaching and Learning in Higher Education.

John O’Donoghue, PhD (1978), University of Loughborough, UK, is Emeritus Associate Professor of Mathematics Education, University of Limerick, Ireland. He has served as chair of Adults Learning Mathematics -- A Research Forum, and contributed to various publications in adult mathematics/numeracy including journal articles, book chapters, and conference proceedings.

Review Quotes

“I recommend this book to anyone with an interest or role in adult education, policy, and work placement, but it should also be of interest to those involved in teaching or education. Furthermore, the fact that this approach can help to remove the invisibility of mathematics for workers in the workplace and show them how they are using it every day, could help to reduce the negative perception of mathematics and increase the recognition of mathematics as a practical skill for all.” -- Dr Ciarán Mac an Bhaird, Department of Mathematics and Statistics, Maynooth University

“This is a good, useful and readable book … provides a variety of case studies which illustrate the invisibility of Maths in workplace and seeks to recognise the mathematics knowledge that exists … The book is well-researched and presents a great array of results. Academics with research interests in the topic may find it both useful and interesting. The contextualisation with both national survey data and case studies from the work shadowing give a good insight into perceptions in relation to maths in the workplace and it is interesting to see the detail in the case studies and how they support or not the survey data. The chapter on research to practice is very welcome and makes many valuable points … Going forward the publication is useful in the context of constructing policy, pedagogy and syllabi understanding the place of Maths in the workplace and were it is both seen and unseen. The tools which were used are well explained and can be practically applied in other studies and the data published here used for comparison. From an employer’s perspective it demonstrates mechanisms which not only identify maths competency required for a role or an individual but can also assist in setting criteria for those changing roles or coming into an organisation. It is also useful in devising training plans.” -- Miriam O’Donoghue, Head of Lifelong Learning, IT Tallaght, Dublin

“There are multiple audiences to whom this work would be valuable. First, and most naturally, the tools developed by the team would be useful to researchers in the field of adult numeracy. The survey is not unique to Irish workers and the connection to the Program for the International Assessment of Adult Competencies (PIACC) and Organization for Economic Cooperation and Development (OECD) key competencies gives it a global flavor and usefulness. Furthermore, the work is situated within a theoretical framework applicable to international vocational and workplace mathematics research. The work represented in the volume could be replicated or extended to include case studies of completely different companies and jobs. On a different level, the findings of the study should be of interest to those individuals planning instruction for adult mathematics students …. Finally, government departments responsible for workplace/vocational education should take note of the disparity between school mathematics which is identifiable and traditionally assessible and the mathematical “ways of thinking” that are critical to even the simplest of the jobs described in the case studies. Workplace and vocational education is expensive in terms of both money and time. The findings reported by the authors in this volume provide valuable evidence that can serve to inform and direct initiatives to advance workplace numeracy well beyond the borders of the Republic of Ireland.”-- Katherine Safford-Ramus, Ed.D., Professor of Mathematics (Ret.), Saint Peter’s University, Jersey City, New Jersey, USA

Table of contents

Diana Coben
List of Figures and Tables

Chapter 1: Introduction: What This Book Is about
 Guide to Structure of the Book

Chapter 2: Adults Using Mathematics in the Workplace: It’s Not Mathematics, It’s Just Common Sense; Part of the Job
 Cultural Historical Activity Theory
 Invisible Mathematics in the Workplace

Chapter 3: Identifying and Measuring Mathematics Invisibility in the Workplace: Stripping away the Layers That Hide What a Person Knows about Mathematics
 Survey Methodology
 Measuring Mathematics Capability
 Measuring Mathematics Capability in the Workplace
 Numerate Behaviour
 Workplace Exploratory Tools
 Job-shadowing Case Studies
 Impact of Mathematics Invisibility

Chapter 4: Broadening the Scope: Design and Key Findings of the National Survey of People at Work
 Characterisation of Workplace Mathematics in the Workplace
 Frequency of Numerate Behaviour
 Quantity and Number
 Shape and Space and Pattern and Relationship
 Data Handling and Chance

Chapter 5: Job Shadowing: Four Case Studies of People Engaged in Their Job
 Job Shadowing People at Work
 Case Study Host Company A
 Research Host Company B
 Case Study 1 Rob
 Case Study 2 Jim
 Case Study 3 ‘Laura’
 Case Study 4 ‘M’
 Mathematics Invisibility in the Workplace
 A Workplace Contextualisation of Mathematics
 Workplace Context-Complexity Protocol

Chapter 6: From Research into Practice: How to Bring the Benefit of Research to Learners
 Extended NFQ Illustrated
 Extended NFQ – Case Study 1
 Extended NFQ – Case Study 2
 Extended NFQ – Case Study 3
 Extended NFQ – Case Study 4
 Recruitment Dichotomy
 Implications: Learners, Curriculum, Tutors, Policy, Standards & RPL
 Research Instruments Modified for Practical Implementation
 How This Approach Works
 Why Does It Matter?



All of those interested in adult education in general and mathematics education in particular, including learners, teachers, researchers, policy makers, curriculum developers, recruiters, change managers, and work placement specialists.

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